Is it possible to use a functional limit as an initial condition in NDsolve

Questions
,
1

Want to get this to work, but it’s saying the system is overdetermined.

m = 7/34169*10^(-6)*mp;
mp = 2.435*10^(18);
k = 8*10^(-41);

NDSolve[{u’’ + (-2/n^2 + k^2 + m^2/H^2/n^2)*u == 0,
Normal[Series[u, {n, Infinity, 0}]] == Exp/(2*k)^(1/2)},
u, {n, 8*10^(38), 1.13*10^(42)}]

2 
m = 7/34169*10^(-6)*mp;

mp = 2.435*10^(18);
k = 8*10^(-41);
H = 1; (* was missing *)

NDSolve[{u''[n] + (-2/n^2 + k^2 + m^2/H^2/n^2)*u[n] == 0, 
  Normal[Series[u[n], {n, Infinity, 0}]] == Exp[(2*k)^(1/2)]}, u, {n, 
  8*10^(38), 1.13*10^(42)}]

NDSolve::overdet: There are fewer dependent variables, {u[n]}, than equations, so the system is overdetermined. >>

is this meant to be a differential equation (why then there are conditions {n, Infinity, 0} outside the range {n, 8 10^38, 1.13 10^42) or is this meant to be a recurrence equation (why then are the derivatives)?

3

It’s a differential equation. I figured you couldn’t put the limit for NDsolve to Infinity. Besides, I don’t care what the function looks like all the way to infinity. I just care that it has that functional form for n → Infinity.